k^2/3=225

Solution for k^2/3=225 equation:

k^2/3=225

We move all terms to the left:

k^2/3-(225)=0

We multiply all the terms by the denominator


k^2-225*3=0

We add all the numbers together, and all the variables

k^2-675=0

a = 1; b = 0; c = -675;
Δ = b2-4ac
Δ = 02-4·1·(-675)
Δ = 2700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{3}}{2*1}=\frac{0-30\sqrt{3}}{2}
=-\frac{30\sqrt{3}}{2}
=-15\sqrt{3}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{3}}{2*1}=\frac{0+30\sqrt{3}}{2}
=\frac{30\sqrt{3}}{2}
=15\sqrt{3}
$